Welcome to the Forum
@realtommcleod ! You've thought through a lot of the details, and having private rooms and luggage transfers will make the potential journey smoother for sure.
Having had four kids, all via c-section (long story), something to think about is if the baby happens to come via c-section, it would be really good to plan for a solid 6 weeks, if not 8 weeks, for new mom to take it easy and completely heal. Doing something too intensive too soon, combined with sleep deprivation, would be hard on the body.
For me, I was able to take short walks around the neighborhood 2 to 3 weeks after each baby was born (the first week or 10 days I was still resting, taking care of the incision, and being on painkillers), building up slowly to longer walks. Knowing the Camino now, I'm not sure I would have been "Camino ready" 8 weeks after any of the babies was born, but that could just be me!
The Inglés is very pretty, but also quite hilly in spots. A recovering mom might have it harder; also just something to be aware of.
Of course, you guys might not have to have a c-section at all...but these are some of my thoughts if you're asking for input
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And it's a great idea to bring your plan to the pediatrician. One suggestion also could be to let the OB/GYN know and see what he/she thinks after the baby is born, as far as how mom is healing.